CN116094894A - A Real Signal Orthogonal Frequency Division Multiplexing Method and Device Applicable to Underwater Communication - Google Patents

Abstract

The present application relates to a real signal orthogonal frequency division multiplexing method and apparatus suitable for underwater communication, the method comprising a transmitter system based on data modulation of discrete hartley transform orthogonal frequency division multiplexing (DHT-OFDM) and a receiver system based on Discrete Fourier Transform (DFT). The method uses the real signal as input, reduces the complexity of complex operation, improves the prior method based on the cyclic prefix and index modulation technology in order to solve the problem of data rate reduction caused by inter-carrier coupling of a discrete Hartley-orthogonal frequency division multiplexing (DHT-OFDM) method, realizes a reliable underwater communication system, reduces pilot frequency overhead by 50% under the condition of not losing channel estimation precision, improves frequency spectrum efficiency, and enhances the error rate performance of the system and the robustness to carrier frequency offset.

Description

A real signal orthogonal frequency division multiplexing method and device suitable for underwater communication

Technical Field

The present application relates to the field of communication technology, and in particular to a real signal orthogonal frequency division multiplexing method and device suitable for underwater communication.

Background Art

Underwater acoustic communication technology is an important core technology in the marine field. As the marine environment is affected by factors such as multipath effect, Doppler effect, carrier frequency offset (CFO), etc., underwater acoustic communication system (UWA) is one of the most complex communication systems. The transmission state of underwater acoustic channels is changeable and the marine operating environment is harsh, which places high demands on communication algorithms and equipment reliability. The transmission rate, transmission bandwidth, and transmission distance of underwater communication limit the application of current underwater communication technology.

Orthogonal frequency division multiplexing (OFDM), as a multi-carrier transmission method, overlaps the sub-channel spectra for parallel data transmission. Without the need for a high-speed equalizer, it can combat narrowband pulse noise and multipath fading while greatly improving channel utilization and meeting the growing demand for data transmission capacity. Therefore, it can be used as a key technology for the next generation of broadband communications. However, in high-speed scenarios, the orthogonality between sub-channels will be destroyed by Doppler frequency shift and cause inter-carrier interference, and the superposition of multiple OFDM sub-channel signals will also result in a higher peak-to-average ratio. These shortcomings make OFDM unsuitable for high-speed scenarios.

This is because UWA communication systems are considered to be untrusted systems considering the two main assumptions represented by the channel effects being constant during each symbol duration and the sparsity of the UWA channel, where the channel can vary over time and sparsity cannot always be assumed. Therefore, standard OFDM-UWA usually inserts frequency domain pilot tones to track the channel effects at the expense of the obtained spectral efficiency. In terrestrial wireless communications, real signal based OFDM has been extensively studied and proved to be superior to DFT-OFDM in many aspects, such as: reduced computational complexity, reduced minimum subcarrier spacing to ensure orthogonality, double the number of subcarriers in the same occupied bandwidth compared to DFT-OFDM, and higher robustness to CFO effects. There are two main real signal based OFDM, which are discrete cosine transform OFDM (DCT-OFDM) and DHT-OFDM.

In MCM and SCM systems, DHT-OFDM outperforms other different triangular transforms. Unlike DFT-OFDM, DHT-OFDM cannot directly diagonalize multipath channels except by coupling the signals on mirror-symmetric subcarriers to each other. This defect is called inter-carrier coupling (ICC) and causes the data rate to drop by half. Therefore, DFT-OFDM is still considered the most popular scheme in time-varying channels because it provides the property to accurately perform the estimation task at the receiving end.

Recently, real signal-based OFDM (such as DCT-OFDM) has also been combined with index modulation (IM) to achieve higher spectral efficiency and/or enhance bit error rate (BER) performance, making it a promising high-spectrum multi-carrier technology for next-generation wireless communications. Unfortunately, these systems cannot be directly used in real communication systems where the channel varies with time, as the estimation task becomes more complex. Compared with DFT-OFDM, the estimation task in MCM based on real signals cannot be performed reliably. This is because the attractive property of channel diagonalization provided by the DFT matrix enables the use of low-complexity and accurate frequency domain channel estimation. However, the prior art attempts to study DCT-OFDM channel estimation using time-domain symmetric training symbols, but it is still necessary to double the guard interval, and in communication systems with long channel delays (such as UWA systems), the IBI problem discussed earlier will be raised again. Therefore, it is of practical significance to enable real signal-based OFDM for UWA communications. On the one hand, a reliable UWA with high robustness to the impact of the marine environment is achieved. On the other hand, the UWA spectrum efficiency is enhanced without any additional hardware or performance degradation. Data rate enhancement in UWA communications is considered to be one of the main challenging tasks due to the characteristics of UWA channels.

Summary of the invention

The present invention proposes a real signal orthogonal frequency division multiplexing method and device suitable for underwater communication. In the underwater communication environment under complex marine environment, the problem of data rate reduction caused by carrier coupling in the discrete Hartley-orthogonal frequency division multiplexing (DHT-OFDM) method is overcome. Based on the cyclic prefix and index modulation technology, the existing method is improved to realize a reliable underwater communication system. Moreover, without losing the channel estimation accuracy, the pilot overhead is reduced by 50%, which not only improves the spectrum efficiency, but also enhances the system's bit error rate performance and robustness to carrier frequency offset, including the following:

In a first aspect, the present application proposes a real signal orthogonal frequency division multiplexing method suitable for underwater communication, the method adopts a transmitter system based on discrete Hartley transform orthogonal frequency division multiplexing data modulation and a receiver system based on discrete Fourier transform, and the method includes:

In the transmitter system:

The original data is distributed to subcarriers through an encoder and an interleaver;

performing digital modulation and index modulation on the processed data;

Add a guard interval to the sequence data and use N-point IDFT to map it to the time domain to obtain time domain data;

The time domain data is transmitted to the UWA channel after up-conversion process;

In the receiver system:

down-converting the Doppler-compensated data stream received from the transmitter;

Performing a DFT process on the data stream after removing the cyclic prefix;

Perform CFO compensation and channel equalization on the data stream after the DFT process;

The processed data is index-demodulated and finally decoded.

Preferably, in the transmitter system, the data modulation of the input signal bit stream is based on

实三角变换来执行；

Real trigonometric transformation is performed;

使得

Where N and E represent the number of DHT-OFDM subcarriers and the DHT-OFDM symbol duration, respectively. The transformation matrix corresponds to the sum of the real and imaginary parts of the DFT matrix. The orthogonality in DHT-OFDM satisfies the minimum carrier spacing.

Make

Preferably, in the receiver system, the complex basis of the acoustic communication Fourier exponential function is used in DFT-OFDM to modulate the data, and the complex basis is specifically:

Where N and T represent the number of DFT-OFDM subcarriers and symbol periods, respectively;

When using a discrete Fourier transform-based receiver system, the time domain modulation data obtained is complex. When using DFT-OFDM, the time domain modulation data obtained is complex, which leads to an increase in the required subcarrier spacing to ensure orthogonality between subcarriers, specifically:

Preferably, in the receiver system, occupying the available UWA bandwidth B with N DFT-OFDM subcarriers spacing F _Δ corresponds to occupying the same bandwidth with N DHT-OFD subcarriers spacing δ _Δ , such that F _Δ =2δ _Δ , n=2N;

The data symbols obtained from modulating X(0), X(1)…, X(n) are modulated using DFT-OFDM and DHT-OFDM respectively, specifically:

where _Xr (n) is the real part of X(n), modulated by any real modulation sequence _Mr.

Preferably, the digital modulation and index modulation of the processed data comprises:

Assume that B bits are the output of the channel encoder that needs to be transmitted in a symbol of length N, and the information bits B are modulated using an M-ary PAM modulation method;

The pilot tone is multiplexed with the data, and the data _Xr (n)=Xr _,d (n)+ _Xr,p (n) is forwarded to the IDHT to obtain the modulated data x(t) as follows:

Preferably, the adding of a guard interval to the sequence data and mapping to the time domain using an N-point IDFT to obtain time domain data comprises:

To avoid ISI, a guard interval is added which should be longer than the maximum delay of the channel. The passband up-converted signal x (t) can be expressed as follows:

Where T _G and T represent the guard interval time and symbol data interval time respectively. Then, the passband signal is transmitted through the UWA channel, specifically:

Preferably, down-converting the Doppler-compensated data stream received from the transmitter comprises:

At the receiving end, the passband received signal y(t) can be expressed as follows:

Channel and CFO estimation is performed based on:

Preferably, the simultaneously performing CFO compensation and channel equalization on the data stream after the DFT process comprises:

The channel is estimated using a least squares formula based on the vector _Rp representing the received pilot tones in the frequency domain and the matrix D _(Xp) representing the diagonal matrix of pilot tone vectors _Xp known to the transmitter and receiver. The estimated time domain impulse response of the channel is given by:

通过上述公式中的估计信道

进行N点快速傅立叶变换来获得，在不丧失通用性的情况下，用最小均方误差频域均衡器用于计算系数

第n个子载波y(n)中的信号被均衡如下：The channel frequency response in this method

The estimated channel in the above formula

Perform an N-point fast Fourier transform to obtain, without losing generality, the minimum mean square error frequency domain equalizer is used to calculate the coefficients

The signal in the nth subcarrier y(n) is equalized as follows:

In a second aspect, the present application also proposes a real signal orthogonal frequency division multiplexing device suitable for underwater communication, characterized in that: the device includes a transmitter system based on discrete Hartley transform orthogonal frequency division multiplexing data modulation and a receiver system based on discrete Fourier transform;

In the transmitter system, the original data is allocated to subcarriers through an encoder and an interleaver;

In the transmitter system, the processed data is digitally modulated and indexed;

In the transmitter system, a guard interval is added to the sequence data and mapped to the time domain using an N-point IDFT to obtain time domain data;

In the transmitter system, the time domain data is transmitted to the UWA channel after an up-conversion process;

In the receiver system, the Doppler-compensated data stream received from the transmitter is down-converted;

In the receiver system, a DFT process is performed on the data stream with the cyclic prefix removed;

In the receiver system, CFO compensation and channel equalization are performed simultaneously on the data stream after the DFT process;

In the receiver system, the processed data is index-demodulated and finally decoded.

In summary, this application at least includes the following beneficial technical effects:

1. The present invention improves the existing method based on cyclic prefix and index modulation technology, realizes a reliable underwater communication system, and reduces the pilot overhead by 50% without losing the channel estimation accuracy, which not only improves the spectrum efficiency, but also enhances the system's bit error rate performance and robustness to carrier frequency offset;

2. Compared with the traditional IM-DFT-OFDM, the OFDM scheme based on real signals (such as IM-DCT-OFDM) of the present invention provides a higher data rate, which can overcome the channel estimation limitation of OFDM based on real signals and obtain higher bandwidth efficiency for UWA communication;

3. The present invention uses real signals as input, reducing the complexity of complex operations. In order to overcome the problem of data rate reduction caused by carrier-to-carrier coupling in the discrete Hartley-orthogonal frequency division multiplexing (DHT-OFDM) method, the present invention improves the existing method based on cyclic prefix and index modulation technology, thereby realizing a reliable underwater communication system. Moreover, without losing the accuracy of channel estimation, the pilot overhead is reduced by 50%, which not only improves the spectrum efficiency, but also enhances the system's bit error rate performance and robustness to carrier frequency offset.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate the embodiments and are used together with the description to explain the principles of the present application. It will be easy to recognize other embodiments and many expected advantages of the embodiments because they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale with each other. The same reference numerals refer to corresponding similar parts.

FIG1 is a flow chart of a real signal orthogonal frequency division multiplexing method suitable for underwater communication according to the present application.

FIG. 2 is a schematic diagram showing a PAPR performance comparison of a real signal orthogonal frequency division multiplexing method suitable for underwater communication in the present application.

FIG3 is a schematic diagram showing a BER performance comparison of a real signal orthogonal frequency division multiplexing method suitable for underwater communication in the present application.

FIG4 is a schematic diagram showing a comparison of BER performances affected by different CFOs in a real signal orthogonal frequency division multiplexing method suitable for underwater communication in the present application.

FIG5 is a schematic diagram showing a BER performance comparison of different IM effects of a real signal orthogonal frequency division multiplexing method suitable for underwater communication in the present application.

DETAILED DESCRIPTION

The present application will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the relevant invention, rather than to limit the invention. It should also be noted that, for ease of description, only the parts related to the relevant invention are shown in the accompanying drawings.

It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

FIG1 shows a flow chart of a real signal orthogonal frequency division multiplexing method suitable for underwater communication in the present application. In combination with reference to FIG1, the method includes a transmitter system based on discrete Hartley transform orthogonal frequency division multiplexing (DHT-OFDM) data modulation and a receiver system based on discrete Fourier transform (DFT). Real signal discrete Hartley transform is used instead of Fourier transform, cyclic prefix technology is used to solve the inter-carrier coupling problem that may be caused by the DHT-OFDM method, index modulation is used in real signal transformation to improve spectrum efficiency and bit error rate, and in order to further improve the spectrum efficiency achieved, the improved IM-DHT-OFDM is used for UWA communication. The method specifically includes the following steps:

Step S1, in the transmitter system, the original data is allocated to subcarriers through an encoder and an interleaver;

Step S2, in the transmitter system, digitally modulating and index modulating the processed data;

In a transmitter system based on discrete Hartley transform orthogonal frequency division multiplexing (DHT-OFDM) data modulation, the subcarrier duration is reduced to half of that of DFT-OFDM, which provides many advantages in terms of CFO, BER and data rate performance.

Assuming that B bits are the output of the channel encoder that needs to be transmitted within a symbol of length N, the information bit B is modulated using an M-ary PAM modulation method because DHT-OFDM is a real signal that generates X _r (n) and then mapped to N = 2N _d + N _p subcarriers, while the pilot tone represented by the PAM modulated data X _r,p (n) is mapped to N _p subcarriers.

Unlike terrestrial wireless communications, multiplexing pilot tones with data is necessary to ensure accurate environmental effect tracking for each subcarrier. The pilot tones are equidistantly distributed with a specific duration to enable channel estimation with a small loss in spectral efficiency, as explained later. Therefore, the data _Xr (n) = _Xr,d (n) + _Xr,p (n) is forwarded to the IDHT to obtain the modulated data x(t) as follows:

Step S3, in the transmitter system, adding a guard interval to the sequence data and mapping it to the time domain using an N-point IDFT to obtain time domain data;

To avoid ISI, a guard interval is added which should be longer than the maximum delay of the channel. The passband up-converted signal x (t) can be expressed as follows:

Where T _G and T represent the guard interval time and symbol data interval time respectively. Then, the passband signal is transmitted through the UWA channel, and the formula is as follows:

Step S4, in the transmitter system, the time domain data is transmitted to the UWA channel after undergoing an up-conversion process;

Additional pilot packets are used to accurately perform channel estimation to mitigate UWA communications from multipath, CFO effects, and environmental noise. Typically, pilot tones are used for the estimation task at the expense of the obtained data rate, which destroys bandwidth efficiency.

In the transmitter system of steps S1 to S4, the system includes a CP-based DHT-OFDM, a real signal discrete Hartley transform instead of Fourier transform, a cyclic prefix technique to solve the inter-carrier coupling problem that may be caused by the DHT-OFDM method, and in order to further improve the achieved spectrum efficiency, a modified IM-DHT-OFDM is used for UWA communication. The data modulation of the input signal bit stream is based on

实三角变换来执行；

Real trigonometric transformation is performed;

使得

Where N and E represent the number of DHT-OFDM subcarriers and the DHT-OFDM symbol duration, the transformation matrix corresponds to the sum of the real and imaginary parts of the DFT matrix, and the orthogonality in DHT-OFDM satisfies the minimum carrier spacing

Make

Step S5, in the receiver system, down-converting the Doppler-compensated data stream received from the transmitter;

At the receiving end, the passband received signal y(t) can be expressed as follows:

The processing of DSF in the received signal is similar to the UWA channel transmit PAS band signal processing modeled in . Therefore, the down-converted resampled received signal is also shown below. Channel and CFO estimation can be performed based on the following:

Step S6, in the receiver system, performing a DFT process on the data stream with the cyclic prefix removed;

Step S7, in the receiver system, performing CFO compensation and channel equalization on the data stream after DFT simultaneously;

Because pilot-based CFO estimation relies on channel estimation, similar to the traditional DFT-OFDM scheme, the least squares (LS) formula is used to estimate the channel. The LS estimation is based on the vector _Rp representing the received pilot tone in the frequency domain. The matrix D _(Xp) represents the diagonal matrix of the pilot tone vector _Xp known to the transmitter and receiver, the matrix V. The estimated time domain impulse response of the channel is given by:

通过上述公式中的估计信道

进行N点快速傅立叶变换(FFT)来获得。在不丧失通用性的情况下，用最小均方误差(MMSE)频域均衡器用于计算系数

第n个子载波y(n)中的信号被均衡如下：In addition, the channel frequency response in this method

The estimated channel in the above formula

Without losing generality, a minimum mean square error (MMSE) frequency domain equalizer is used to calculate the coefficients

The signal in the nth subcarrier y(n) is equalized as follows:

The received signals at the subcarriers carrying the pilots are considered known. When assuming an ideal CFO, the equalized data in these subcarriers are equal to the pilot tones known to the transmitter and receiver. Based on this similarity, a preliminary CFO estimation and compensation is performed.

Step S8, in the receiver system, index demodulation and final decoding of the processed data;

In the receiver system of steps S5 to S8, the data is modulated using the complex basis of the acoustic communication Fourier exponential function, which can be written as follows:

Where N and T represent the number of DFT-OFDM subcarriers and symbol periods, respectively. When using DFT-OFDM, the time-domain modulated data obtained are all complex, which leads to an increase in the required subcarrier spacing to ensure orthogonality between subcarriers, for example:

Therefore, occupying the available UWA bandwidth B (Hz) with N DFT-OFDM subcarriers with a spacing of F _Δ corresponds to occupying the same bandwidth with N DHT-OFD subcarriers with a spacing of δ _Δ , so that F _Δ = 2δ _Δ , n = 2N. In other words, the available bandwidth occupied by N DFT-OFDM subcarriers can be divided into 2N narrow DHT-OFDM subcarriers while maintaining perfect reconstruction conditions. Therefore, the data symbols obtained from the modulation X(0), X(1) ..., X(n) are modulated using DFT-OFDM and DHT-OFDM, respectively, as shown below:

where _Xr (n) is the real part of X(n), modulated by any real modulation sequence _Mr , such as pulse amplitude modulation (PAM), and packed into subcarriers indexed by n.

Compared with the traditional IM-DFT-OFDM, the OFDM scheme based on real signals (such as IM-DCT-OFDM) of the present application provides a higher data rate, which can overcome the channel estimation limitations of OFDM based on real signals and obtain higher bandwidth efficiency for UWA communications.

Based on an orthogonal frequency division multiplexing method based on real signals suitable for underwater communication disclosed in the embodiment of the present application, the following performance is obtained by MATLAB modeling and simulation calculation:

From Figure 2, we can see the PAPR performance of the proposed scheme compared to the traditional benchmark. It is clear that the PAPR of the real signal based scheme is 2dB higher than the traditional DFT-OFDM scheme, which is expected due to the superposition of twice the number of subcarriers in the OFDM symbol. The IM scheme also inherits the same PAPR performance of the traditional scheme, although a higher data rate is achieved in the proposed scheme. The proposed IM scheme can provide better bit error rate, robustness against CFO, and spectral efficiency compared to standard DFT-OFDM and IM-DFT-OFDM.

Figure 3 shows the BER performance with an ideal CFO effect to evaluate the channel estimation effect and the effect of improving the achieved data rate. The pilot insertion in OFDM-IM is performed in the same way as DHTOFDM. This means that we first map the IM to the data subcarriers and then insert the pilots into the frequency domain subcarriers. The number of active subcarriers, Ko _, is set to have the spectral efficiency of conventional DFT-OFDM. On the other hand, DHTOFDM and IM-DHT-OFDM achieve a 16.67% higher data rate when _No = 4, _Ko = 2 or _Ko = 8, _Ko = 3 due to the reduction caused by pilot grouping, while IM-DHT-OFDM ( _No = 4, _Ko = 3 or _No = 8, _Ko = 4) achieves up to 45.83% data rate improvement. Although the proposed schemes achieve higher data rates, all schemes have almost similar bit error rate performance.

The CFO effect is one of the main problems encountered in UWA communications, this effect cannot always be perfectly estimated and such a robust scheme against CFO is highly desired. Figure 4 shows the BER performance at different CFO values and it is clear that the proposed scheme is more resistant to the CFO effect due to the authenticity of the transmitted signal. The higher the CFO effect, the more improvement the proposed scheme obtains. At CFO = 0.2, DFT-OFDM is unable to recover the performance while the proposed scheme still provides acceptable performance, which makes our introduced method more likely to be used for untrusted communications including UWA communications. Figure 5 illustrates the impact of the size of K _o and the number of active subcarriers on the BER performance, proving that the proposed method is an ideal choice.

As an implementation of the above-mentioned method, the present application provides an embodiment of a real signal orthogonal frequency division multiplexing device suitable for underwater communication, and the device embodiment corresponds to the method embodiment of the first aspect, and the device includes a transmitter system based on discrete Hartley transform orthogonal frequency division multiplexing data modulation and a receiver system based on discrete Fourier transform;

In the transmitter system, the original data is allocated to subcarriers through an encoder and an interleaver;

In the transmitter system, the processed data is digitally modulated and indexed;

In the transmitter system, a guard interval is added to the sequence data and mapped to the time domain using an N-point IDFT to obtain time domain data;

In the transmitter system, the time domain data is transmitted to the UWA channel after an up-conversion process;

In the receiver system, the Doppler-compensated data stream received from the transmitter is down-converted;

In the receiver system, a DFT process is performed on the data stream with the cyclic prefix removed;

In the receiver system, CFO compensation and channel equalization are performed simultaneously on the data stream after the DFT process;

In the receiver system, the processed data is index-demodulated and finally decoded.

In the description of the present application, it should be understood that the terms "upper", "lower", "inside", "outside", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, which are only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. The word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "one" or "an" preceding an element does not exclude the presence of multiple such elements. The simple fact that certain measures are recorded in mutually different dependent claims does not indicate that a combination of these measures cannot be used for improvement. Any reference symbols in the claims should not be interpreted as limiting the scope.

Claims (9)

1. A real signal orthogonal frequency division multiplexing method suitable for underwater communication, characterized in that the method adopts a transmitter system based on discrete Hartley transform orthogonal frequency division multiplexing data modulation and a receiver system based on discrete Fourier transform, and the method comprises: In the transmitter system: The original data is distributed to subcarriers through an encoder and an interleaver; performing digital modulation and index modulation on the processed data; Add a guard interval to the sequence data and use N-point IDFT to map it to the time domain to obtain time domain data; The time domain data is transmitted to the UWA channel after up-conversion process; In the receiver system: down-converting the Doppler-compensated data stream received from the transmitter; Performing a DFT process on the data stream after removing the cyclic prefix; Perform CFO compensation and channel equalization on the data stream after the DFT process; The processed data is index-demodulated and finally decoded. 2. The real signal orthogonal frequency division multiplexing method suitable for underwater communication according to claim 1, characterized in that: In the transmitter system, the data modulation of the input signal bit stream is based on

Real trigonometric transformation is performed; Where N and E represent the number of DHT-OFDM subcarriers and the DHT-OFDM symbol duration, respectively. The transformation matrix corresponds to the sum of the real and imaginary parts of the DFT matrix. The orthogonality in DHT-OFDM satisfies the minimum carrier spacing.

Make

3. The real signal orthogonal frequency division multiplexing method suitable for underwater communication according to claim 2, characterized in that: In the receiver system, the complex basis of the acoustic communication Fourier exponential function is used in DFT-OFDM to modulate the data, and the complex basis is specifically:

Where N and T represent the number of DFT-OFDM subcarriers and symbol periods, respectively; When using a discrete Fourier transform-based receiver system, the time domain modulation data obtained is complex. When using DFT-OFDM, the time domain modulation data obtained is complex, which leads to an increase in the required subcarrier spacing to ensure orthogonality between subcarriers, specifically:

4. The real signal orthogonal frequency division multiplexing method suitable for underwater communication according to claim 3, characterized in that: In the receiver system, occupying the available UWA bandwidth B with N DFT-OFDM subcarrier spacing F _Δ corresponds to occupying the same bandwidth with N DHT-OFD subcarrier spacing δ _Δ , such that F _Δ =2δ _Δ , n=2N; The data symbols obtained from modulating X(0), X(1)…, X(n) are modulated using DFT-OFDM and DHT-OFDM respectively, specifically:

where _Xr (n) is the real part of X(n), modulated by any real modulation sequence _Mr. 5. A real signal orthogonal frequency division multiplexing method suitable for underwater communication according to claim 1, characterized in that: the digital modulation and index modulation of the processed data comprises: Assume that B bits are the output of the channel encoder that needs to be transmitted in a symbol of length N, and the information bits B are modulated using an M-ary PAM modulation method; The pilot tone is multiplexed with the data, and the data _Xr (n)=Xr _,d (n)+ _Xr,p (n) is forwarded to the IDHT to obtain the modulated data x(t) as follows:

6. A real signal orthogonal frequency division multiplexing method suitable for underwater communication according to claim 1, characterized in that: adding a guard interval to the sequence data and using N-point IDFT to map to the time domain to obtain time domain data comprises: To avoid ISI, a guard interval is added which should be longer than the maximum delay of the channel. The passband up-converted signal x(t) can be expressed as follows:

Where T _G and T represent the guard interval time and symbol data interval time respectively. Then, the passband signal is transmitted through the UWA channel, specifically:

7. A real signal orthogonal frequency division multiplexing method suitable for underwater communication according to claim 1, characterized in that: the down-conversion of the Doppler-compensated data stream received from the transmitter comprises: At the receiving end, the passband received signal y(t) can be expressed as follows:

Channel and CFO estimation is performed based on:

8. A real signal orthogonal frequency division multiplexing method suitable for underwater communication according to claim 1, characterized in that: the simultaneous CFO compensation and channel equalization of the data stream after the DFT process comprises: The channel is estimated using a least squares formula based on the vector _Rp representing the received pilot tones in the frequency domain and the matrix D _(Xp) representing the diagonal matrix of pilot tone vectors _Xp known to the transmitter and receiver. The estimated time domain impulse response of the channel is given by:

The channel frequency response in this method

The estimated channel in the above formula

Perform an N-point fast Fourier transform to obtain, without losing generality, the minimum mean square error frequency domain equalizer is used to calculate the coefficients

The signal in the nth subcarrier y(n) is equalized as follows:

9. A real signal OFDM device suitable for underwater communication, characterized in that: the device comprises a transmitter system for data modulation based on discrete Hartley transform OFDM and a receiver system based on discrete Fourier transform; In the transmitter system, the original data is allocated to subcarriers through an encoder and an interleaver; In the transmitter system, the processed data is digitally modulated and indexed; In the transmitter system, a guard interval is added to the sequence data and mapped to the time domain using an N-point IDFT to obtain time domain data; In the transmitter system, the time domain data is transmitted to the UWA channel after an up-conversion process; In the receiver system, the Doppler-compensated data stream received from the transmitter is down-converted; In the receiver system, a DFT process is performed on the data stream with the cyclic prefix removed; In the receiver system, CFO compensation and channel equalization are performed simultaneously on the data stream after the DFT process; In the receiver system, the processed data is index-demodulated and finally decoded.

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